Elucidation of the dynamics and transition phenomena in oscillator networks including inactive elements

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400401
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Osaka Prefecture University
• Principal Investigator: Daido Hiroaki 大阪府立大学, 工学(系)研究科(研究院), 教授 (70188465)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 結合振動子系 / ネットワーク / エイジング転移 / 興奮性 / 同期転移 / ヒステリシス

Outline of Final Research Achievements

The present study focuses on the behaviors of globally (i.e., all-to-all) coupled dynamical units, each of which shows either excitability or oscillation depending on its bifurcation parameter. Excitability means returning to a stable fixed point after large deviations from it when the magnitude of perturbation exceeds a threshold. Any increase in the ratio of inactive (here, excitable) units in the system is defined as "aging", which causes an aging transition from the dynamic phase to the static one. The control parameters are the coupling strength and the average of bifurcation parameters of all units. The main results are theoretical explanations of the bifurcation structure and scaling laws of order parameters near the aging transition boundary in the phase diagram. The boundary in the dynamic phase is also theoretically derived. Another subject is the susceptibility of large populations of coupled phase oscillators, whose expression is theoretically obtained.

Free Research Field

非線形動力学